1. Field of Invention
This invention generally relates to puzzles, more specifically to that class of puzzles wherein the object is to fill in a geometric structure with indicia using provided clues and guided by placement rules.
2. Background of the Invention
Puzzles requiring the placement of numbers or symbols in a predetermined grid based on clues and guided by placement rules are common in the prior art. The present invention uniquely combines concepts previously implemented in the following three puzzles—Sudoku, Kakuro, and U.S. Pat. No. 1,121,697 to Weil (1914). The background and limitations for each of these prior art references will be addressed in the following paragraphs:
SUDOKU puzzles are well known in the prior art. Sudoku puzzles are logic puzzles that generally use numbers and a square grid (usually nine-by-nine squares). In its most common form, Sudoku groups the squares into nine boxes, each containing a three-by-three grid of squares. Clues are provided in the form of examiner-selected squares which are prefilled with correctly placed numbers. The goal of Sudoku is, given only the provided clues, to fill in the entire grid so the numbers 1 through 9 appear just once in every row, column, and three-by-three box.
Sudoku is wildly popular, but it's solving techniques are limited to those that rely only on positional logic, that is, correct answers are resolved based on the relative positions of previously determined numbers within the puzzle grid. For example, if a number ‘5’ is already placed in the grid, the number ‘5’ cannot be placed again in the same row or same column. There is no arithmetic required—in fact, it makes no difference whether numbers or any other unique symbols are used as indicia.
Another limitation is that Sudoku does not work with the diagonals formed by the grid. All attention in the puzzle is focused only on rows, columns, and three-by three square grids.
KAKURO puzzles are also known in the prior art. Kakuro puzzles are mathematical puzzles that are very similar to traditional crossword puzzles except numbers are used rather than letters and the only clues provided are the arithmetic sum of the integers in each row or column. The fundamental defining rule for Kakuro is that no integer is allowed to be repeated in any row or column. The goal of Kakuro is to fill in an entire crossword-like grid structure given only the sums for the rows and columns.
Kakuro puzzles are also very popular, but their solving techniques are limited to unique arithmetic summing—techniques that rely on excluding possibilities based on the fixed number of valid numerical combinations of the digits 1 through 9. For example, if the puzzle shows that the numbers in the two squares of a given row must add up to the number “4”, the solution numbers must by “1” and “3” (“2” and “2” is not acceptable because duplicate numbers are not allowed). It cannot yet be determined which square holds the “1” and which square holds the “3”—that information must be determined using the same process against the appropriate columns. However, the initial clue leads to the elimination of 7 of the 9 possible integers. Kakuro puzzles do not rely on positional logic directly. Although it is possible to narrow possibilities based on relative locations in the puzzle grid, the only way to confirm the location of a potential integer is to ensure it sums correctly in the appropriate row and column.
Kakuro shares the limitation described for Sudoku in that it does not recognize the diagonals that are formed by the crossword grid.
The puzzle patented in 1914 by Weil (U.S. Pat. No. 1,121,697) described a 3 by 3 grid of squares with positions for numbers in the corners of each square. Examinees are asked to place the integers 1 through 4 in the corner positions of each square (without repetition within each square) such that the sums of the rows, columns, and diagonals all add up to fifteen.
Weil's puzzle introduces two components that I have incorporated into the present invention. The first is the inclusion of major diagonals as an additional defining component of the puzzle (although Weil's puzzle did not extend to using the shorter diagonals as potential clue sources or puzzle constraints). The second technique I incorporated from Weil is to allow, in certain instances, repetition of numbers when adding them together to form given sums. Allowing multiple (up to 2) “1”s, “2”s, “3”s, or “4”s significantly increased the number of possible valid solution sets, thus increasing the complexity of the resulting puzzle.
The primary limitation of Weil's puzzle, from the perspective of the present invention, is that he did not consider the value of expanding the basic structure of his puzzle beyond squares as the basic building block. The first embodiment of the present invention demonstrates significant advantages in terms of increasing the number of techniques required to solve a placement puzzle by applying the fundamental ideas of Weil's invention to a grid of octagons and introducing additional clues based on the minor diagonals and the diamonds formed by the intersection of the octagons.